First Pair Classified of checked

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_DiskEnumeration_Definitions
import Definitions.Def_D1Bound5_OneSmallFiniteCheck_Definitions

section
namespace D1Bound5
open QuadInt













theorem _root_.D1Bound5.firstPairClassified_of_checked {tau nu : ℤ}
    (hd : 0 < discriminant tau nu)
    (small roots : List (QuadInt tau nu))
    (rows : List ((ℤ × ℤ) × (ℤ × ℤ)))
    (hsmall : ∀ a ∈ disk tau nu 8, a ∈ small)
    (hroots : ∀ q ∈ disk tau nu 8, q ∈ roots)
    (hcheck : firstPairClassifiedBool small roots rows = true)
    (a b : QuadInt tau nu) (hnorm : FirstPairNorms a b)
    (hroot : ∃ q, q*q = a*b+1) :
    (a = 1 ∧ b = 3) ∨ (a = -1 ∧ b = -3) ∨ firstPairCoordinates a b ∈ rows := by sorry









end D1Bound5
end